The minimal supersymmetric model has two complex doublets of Higgs bosons. The resulting physical states are two scalars [${{\mathit H}_{{{1}}}^{0}}$ and ${{\mathit H}_{{{2}}}^{0}}$, where we define ${\mathit m}_{{{\mathit H}_{{{1}}}^{0}}}$ $<$ ${\mathit m}_{{{\mathit H}_{{{2}}}^{0}}}$], a pseudoscalar (${{\mathit A}^{0}}$), and a charged Higgs pair (${{\mathit H}^{\pm}}$). ${{\mathit H}_{{{1}}}^{0}}$ and ${{\mathit H}_{{{2}}}^{0}}$ are also called ${{\mathit h}}$ and ${{\mathit H}}$ in the literature. There are two free parameters in the Higgs sector which can be chosen to be ${\mathit m}_{{{\mathit A}^{0}}}$ and tan $\beta $ = $\mathit v_{2}/\mathit v_{1}$, the ratio of vacuum expectation values of the two Higgs doublets. Tree-level Higgs masses are constrained by the model to be ${\mathit m}_{{{\mathit H}_{{{1}}}^{0}}}{}\leq{}{\mathit m}_{{{\mathit Z}}}$, ${\mathit m}_{{{\mathit H}_{{{2}}}^{0}}}{}\geq{}{\mathit m}_{{{\mathit Z}}}$, ${\mathit m}_{{{\mathit A}^{0}}}{}\geq{}{\mathit m}_{{{\mathit H}_{{{1}}}^{0}}}$, and ${\mathit m}_{{{\mathit H}^{\pm}}}{}\geq{}{\mathit m}_{{{\mathit W}}}$. However, as described in the review on “Status of Higgs Boson Physics” in this Volume these relations are violated by radiative corrections.
The observed signal at about 125 GeV, see section “${{\mathit H}}$'', can be interpreted as one of the neutral Higgs bosons of supersymmetric models. Unless otherwise noted, we identify the lighter scalar ${{\mathit H}_{{{1}}}^{0}}$ with the Higgs discovered at 125 GeV at the LHC (AAD 2012AI, CHATRCHYAN 2012N).
Unless otherwise noted, the experiments in ${{\mathit e}^{+}}{{\mathit e}^{-}}$ collisions search for the processes ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit H}_{{{1}}}^{0}}{{\mathit Z}^{0}}$ in the channels used for the Standard Model Higgs searches and ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit H}_{{{1}}}^{0}}{{\mathit A}^{0}}$ in the final states ${{\mathit b}}{{\overline{\mathit b}}}{{\mathit b}}{{\overline{\mathit b}}}$ and ${{\mathit b}}{{\overline{\mathit b}}}{{\mathit \tau}^{+}}{{\mathit \tau}^{-}}$. Unless otherwise stated, the following results assume no invisible ${{\mathit H}_{{{1}}}^{0}}$ or ${{\mathit A}^{0}}$ decays. Unless otherwise noted, the results are given in the m${}^{max}_{h}$ scenario, CARENA 2013.
In ${{\mathit p}}{{\overline{\mathit p}}}$ and ${{\mathit p}}{{\mathit p}}$ collisions the experiments search for a variety of processes, as explicitly specified for each entry. Limits on the ${{\mathit A}^{0}}$ mass arise from these direct searches, as well as from the relations valid in the minimal supersymmetric model between ${\mathit m}_{{{\mathit A}^{0}}}$ and ${\mathit m}_{{{\mathit H}_{{{1}}}^{0}}}$. As discussed in the review on “Status of Higgs Boson Physics” in this Volume, these relations depend, via potentially large radiative corrections, on the mass of the ${{\mathit t}}~$quark and on the supersymmetric parameters, in particular those of the stop sector. These indirect limits are weaker for larger ${{\mathit t}}$ and ${{\widetilde{\mathit t}}}$ masses. To include the radiative corrections to the Higgs masses, unless otherwise stated, the listed papers use theoretical predictions incorporating two-loop corrections and beyond (SLAVICH 2021), and the results are given for the ${{\mathit M}}{}^{125}_{h}$ benchmark scenario, see BAGNASCHI 2019.